Abstract
This paper presents a new full-vectorial finite-element method in a local cylindrical coordinate system, to effectively analyze bending losses in photonic wires. The discretization is performed in the cross section of a three-dimensional curved waveguide, using hybrid edge/nodal elements. The solution region is truncated by anisotropic, perfectly matched layers in the cylindrical coordinate system, to deal properly with leaky modes of the waveguide. This approach is used to evaluate bending losses in silicon wire waveguides. The numerical results of the present approach are compared with results calculated with an equivalent straight waveguide approach and with reported experimental data. These comparisons together demonstrate the validity of the present approach based on the cylindrical coordinate system and also clarifies the limited validity of the equivalent straight waveguide approximation.
Highlights
The realization of high-density on-chip integration of optical components, or microphotonics, has been the subject of intense investigation in the new technological era
Modal approaches to bending waveguides, such as these based on the finite difference method [16,17,18] and the finite element method (FEM) [19,20,21,22], can be more efficient, because the solution regions decrease to two-dimensional cross sections
This paper proposes a full-vectorial FEM based on the cylindrical coordinate system (CCS) for efficient and accurate analysis of photonic wire bends
Summary
The realization of high-density on-chip integration of optical components, or microphotonics, has been the subject of intense investigation in the new technological era. Modal approaches to bending waveguides, such as these based on the finite difference method [16,17,18] and the finite element method (FEM) [19,20,21,22], can be more efficient, because the solution regions decrease to two-dimensional cross sections These modal approaches provide insights into the physical basis of bending losses in each individual eigenmode. In the curved rib waveguide, that the difference in the calculated effective indices between the ESW approximation and the CCS approach becomes significant when the bending radii reach several micrometers, the difference in the calculated losses is still insignificant [17, 22] In this context, this paper proposes a full-vectorial FEM based on the CCS for efficient and accurate analysis of photonic wire bends.
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